Formal learning theory poses the question of how agents should use observations about their environment to arrive at accurate and true conclusions. To answer this question, empirical and formal inquiries have been provided with topological models in Domain Theory [1, 16], Formal Learning Theory [3], Epistemology and Philosophy of Science [2, 7, 15]. The goal of our work is to present the initial steps of how precisely the topological formalization of empirical inquiry may be expressed in terms of abstract model theory. In this framework, following Genin and Kelly [5, 6], we define what is a method, as well as verifiability, refutability, decidability and limiting verifiability of a proposition. Furthermore, we define what is an abstract empirical problem, and its solvability. We prove that verifiability, refutability, decidability, and limiting verifiability of a proposition and solvability of a problem are invariant under change of notation.